Sinn Féin has secured the single biggest number of first preference votes in Northern Ireland's local government elections, while across the border in the Republic it won 15% of the vote and its highest number of councillors.

The electoral success brings a step closer Gerry Adams' strategic plan to be in government on both sides of the Irish border by 2016 – the centenary of the Easter Rising.

It also suggests that his recent arrest in connection with the IRA's kidnapping, killing and secret burial of Jean McConville did not seriously damage Sinn Féin's election campaign. But the overall unionist vote in Northern Ireland also held up, with the Democratic Unionist party winning 130 seats compared with Sinn Féin, which returns to the new council chambers with 105 seats.

The Ulster Unionist party, after a decade of being eclipsed by the DUP, recovered with 88 councillors and an increase in its share of the vote. Amid Sinn Féin successes in the new Derry/Strabane council there was support for candidates linked to anti-ceasefire republicans. Four dissident/independent republican councillors were elected to the council, including former Real IRA prisoner Gary Donnelly.

Donnelly topped the poll in a working-class ward on Derry's west bank of the river Foyle with 1,154 first preference votes, although Sinn Féin is now the largest party in the newly merged council in the north-west of Northern Ireland.

Commenting on his party's gains south of the border, Adams said: "Sinn Féin hasn't had this strength since 1918," – a general election that took place two years after the Easter Rising and ushered in four years of nationwide violence with war against the British followed by a civil war.

As well as Sinn Féin, leftwing independent candidates did well in the elections on both sides of the border with smaller parties gaining 20% of the vote. Socialist candidate Ruth Coppinger also beat off a strong challenge from Sinn Féin to win a parliamentary by-election in Dublin West this weekend.

In Northern Ireland, the first minister, Peter Robinson, said the DUP's strong showing had "put on notice" Naomi Long, the Alliance party MP for East Belfast who won the seat from him in the last general election. Robinson also said the improvement in the unionist vote demonstrated the need for joint unionist candidates at the UK general election next year.

However, the Alliance party confounded predictions that its support for changing the policy of flying the union flag atop Belfast city hall 365 days a year would lead to electoral meltdown. Long's husband, Michael, topped the poll in east Belfast with the Alliance securing eight councillors in the city. The party once again holds the balance of power between unionists and nationalists on Belfast city council.

Counting resumes on Monday morning for the European elections in Northern Ireland with Sinn Féin and the DUP guaranteed to retain their seats. The UUP predicted on Sunday that its sitting MEP, Jim Nicholson, would also hold his seat but he faces a challenge for the final seat from Jim Allister, the leader of the hardline Traditional Unionist Voice party.

• This article was amended on 27 May 2014 to correct the share of the vote Sinn Féin won in Ireland's local government elections, and mispellings of the names of Jim Allister, and Ruth Coppinger.